Bearings are critical components in the smooth operation of equipment such as industrial machinery and their response to operating temperature and other effects like cavitation and shear thinning play a significant role in overall performance. These small, unassuming parts prevent friction between components during relative movement, carrying loads between a rotor and its case with as little wear as possible and ultimately extending equipment lifetime through reduced fatigue.
With increasing performance, efficiency, and reliability needs from equipment manufacturers come demands for newer and better bearings. Due to more recent factors such as fuel consumption and environmental impact, the demand for low friction bearings has earned particularly high priority. Industrial applications require high-performance bearings to offer reliable operation at high speeds, motion accuracy, low power loss, and minimal noise levels. On the material side, high wear resistance, toughness, and excellent fatigue resistance are also critical needs. Even small variations in the complex interactions between a damaged bearing and the rest of a system can result in multicomponent system failure—extending the significance of bearing reliability beyond simply the bearings themselves.
Hence, a holistic design approach has become a necessity. Designers must focus on load-carrying capacity, but also the effects of temperature rise, power loss, misalignment, starvation in the bearings, housing flexibility, vibration and stability of the equipment, speed variations, and thermal expansion when predicting a bearing’s performance. Simulation tools like the COMSOL Multiphysics® software allow engineers to account for the impact of various physics phenomena simultaneously, help in assessing the significance of such variables early in the design process, and let manufacturers reduce the number of prototype iterations before finalising their products.
Oil film bearing design: An Example
We will see that many design considerations must be taken into account in order to reach the optimal configuration of a bearing system. As an example, the simple shaft bearing system shown in Figure (1) contains oil film bearings as end supports. We’ll take a look at the thermal, fluid, and mechanical behaviour of the entire system and study how these different questions are interdependent.
Operating temperature and viscosity
Shearing of the lubricant due to relative motion between the shaft and bearings causes viscous heat dissipation in the bearing, increasing the operating temperature. Heat generated in the lubricant is conducted to the shaft and bearing surfaces, and finally convected to the atmosphere through the exposed regions. The overall heat balance determines the equilibrium temperature of the lubricant. Additionally, the viscosity of the lubricant depends on the operating temperature and the shearing rate, so these factors must also be considered when determining the equilibrium temperature. Both of these effects reduce the load-carrying capacity of the bearing.
Figure 2(a) shows the effect of temperature and shear thinning on the minimum film thickness, which reduces by 5 to 6 percent when the length-to-radius ratio reaches 2. A lower minimum film thickness indicates lower load-carrying capacity and also poses difficulties in avoiding dry lubrication conditions for tighter manufacturing tolerances. A higher aspect ratio between length and radius can compensate for the reduction in the load-carrying capacity and avoid the dry lubrication conditions.
Another effect of the reduced film thickness is higher pressure gradients. This can cause cavitation problems in the bearings and increased leakage, as shown in Figure 2(b). Longer bearings can be used to minimise the leakage, which of course avoids wasted lubricant, but also increases the recirculation of heated lubricant in the bearing—thus increasing the overall operating temperature.
To mitigate this, a separate outlet port for removing hot oil from the bearing system and an inlet for supplying a cool oil can work together to ensure a lower operating temperature. Hot oil taken from the system may be filtered, cooled, and returned to the bearing to minimise lubricant waste.
At the cost of reduced performance, one positive effect of the temperature rise and shear thinning is a reduction in the heat generated in the bearing, as shown in Figure 2(c). Increasing the length-to-radius aspect ratio again increases the heat loss, because more lubricant experiences shear. Thus, the operating temperature also increases for higher aspect ratios as shown in Figure 2(d).
This study clearly demonstrates that the temperature dependent viscosity and the shear thinning effect reduce the overall operating temperature but also the load-carrying capacity of the bearing. As the lubricant viscosity decreases with increases in temperature, the viscous heat generated in the lubricant is reduced, thus reducing the overall temperature rise. Hence, dependence of the viscosity on temperature mitigates the rise in temperature due to viscous shearing and it is important to account for a correct prediction of the operating temperature. An engineer designing such a bearing must search for the best combination of leakage, operating temperature, and load-carrying capacity for the specific use case.
Effects of cavitation
Another important phenomenon that can drastically affect a bearing’s performance is the cavitation of the lubricant in the divergent part of the film due to a sudden reduction in pressure. From the simulation result, one can clearly see that the load-carrying capacity of the bearing decreases significantly when cavitation effects are accounted for.
This effect is most significant in short bearings. Lubricant leakage also increases moderately due to cavitation in the film, as per the simulation result. A lower minimum film thickness along with cavitation gives rise to a higher pressure gradient, which is responsible for the increase in heat generated in the bearing. Therefore, power loss and maximum temperature both increase with the cavitation.
For short bearings this effect dominates due to cavitation occurring in the larger area of the film. In longer bearings, the pressure gradients are moderate and cavitation can be avoided in the larger part of the bearing.
Effect of rotor-bearing coupling
Finally, the film thickness changes due to deformation of structural components such the journal and bushing. This in turn changes the pressure distribution. Lubricant pressure acts as an external load on the journal and bushing surfaces. Therefore, there is a bidirectional coupling between the fluid film pressure and the relative motion of the journal and bushing surfaces.
Generally, the effects of the bearings are linearized for harmonic studies, assuming an equivalent stiffness and damping coefficients of the bearing at a given rpm, and static loading conditions. Natural modes of the rotor at 3000 rpm for the rotor bearing system are compared for rigid and flexible bearings from the simulation result.
In the first case, the rotor is considered rigidly supported at the bearing locations. In the second case, the flexibility in the bearing and foundation is included in the model with a bearing stiffness 1e8 N/m and a foundation stiffness of 4e8 N/m.When the bearing is rigid, cylindrical and conical modes of the rotor are missed. Also, the natural frequency of the whole system in the first bending mode decreases by 20% due to the bearing flexibility.
Campbell plots for both rigid and flexible bearing cases are shown in Figure 3. For the rigid bearings, no critical speed is found for the rotor below 20000 rpm. However, when the flexibility of both the bearing and foundation are introduced, there are four critical speeds — two for the backward whirl mode shown as the intersection of ω=2Ω and the increasing eigenfrequency curves, and two for the forward whirl mode, shown as the intersection of the decreasing eigenfrequency curve and the x-axis.
This exercise emphasises that the flexibility of the bearing cannot be ignored when identifying the critical speeds; rather bearings are an integral part of the rotor system. By parametrically varying the stiffness of the bearing, this analysis can be repeated to obtain the variations in critical speeds with respect to bearing stiffness, helping designers to choose the appropriate bearing geometry and material parameters for safe operation.
Rotor whirl and minimum film thickness
Whirling of the rotor in the bearing also changes the minimum film thickness. In the steady state, the minimum film thickness experiences harmonic variation with time. Since the minimum film thickness needs to be greater than the surface roughness of the mating surfaces to maintain the film lubrication condition, these dynamic effects must be accounted for during design.
Motion of the journal and bearing due to the shaft whirl, if large, can also impact the minimum film thickness significantly. A stress plot of the rotor bearing system operating under gravity along with the central disk with small eccentricity is obtained from the simulation result that compares the effect of the flexibility of the foundation, or bearing mount, on the minimum film thickness. When the foundation is flexible the mean value of the minimum film thickness reduces by 0.1%.
Deformation becomes more significant in a multi-cylinder engine crankshaft due to the phase difference between the pressure variations in different cylinders, which causes significant bending as shown in Figure 4(a). In such a case the film thickness and the pressure vary significantly in the axial direction as shown in Figure 4(b).
Forward-thinking solutions to industry needs
As the demand for performance, efficiency, and the capacity of rotating machinery continues to increase, bearings must function reliably and safely under a wide variety of operating conditions. A conventional approach to bearing design for supporting a given load is no longer sufficient; rather, a more holistic approach of considering bearings a part of a complex system and their interactions with neighboring components must be considered.
Analysis tools like COMSOL Multiphysics® software, which enables the automatic coupling of interrelated physics phenomena, aid the design process through accurate assessment of bearing interactions with other components. Designers and manufacturers greatly benefit from such tools early in the design process, reducing the number of prototypes, predicting mechanical behavior under different scenarios and for different needs, and ultimately ensuring faster delivery of high quality products in the market.
The article is authored by Prashant Srivastava, Product Manager (Rotor Dynamics Module), COMSOL Multiphysics